When ' $\mathrm{x}^{\prime} \times 10^{-2} \mathrm{~mL}$ methanol (molar mass $=32 \mathrm{~g}$; density $=0.792 \mathrm{~g} / \mathrm{cm}^{3}$ ) is added to 100 mL water (density $=1 \mathrm{~g} / \mathrm{cm}^{3}$ ), the following diagram is obtained. $\mathrm{x}=$ ............. (nearest integer) [Given: Molal freezing point depression constant of water at $273.15 \mathrm{~K}^{\circ}$ is $1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ]

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Solutions

When '

x^{'} \times 1 0^{- 2} mL

methanol (molar mass

= 32 g

; density

= 0.792 g / cm^{3}

) is added to 100 mL water (density

= 1 g / cm^{3}

), the following diagram is obtained.

x =

............. (nearest integer)
[Given: Molal freezing point depression constant of water at

273.15 K^{\circ}

1.86 K kg mol^{- 1}

]

Answer: 543

Solution

Depression in freezing point

Δ T_{f} = 273.15 - 270.65 = 2.5

K. From

Δ T_{f} = K_{f} m

m = \frac{2.5}{1.86} = 1.344 mol/kg

. With

100

mL (

= 0.1

kg) water, moles of methanol

= 1.344 \times 0.1 = 0.1344

mol, mass

= 0.1344 \times 32 = 4.30

g, volume

= \frac{4.30}{0.792} = 5.43

= 543 \times 1 0^{- 2}

mL, so

x = 543

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Solutions →

More JEE Main questions on Solutions

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $PQ_{2}$ . When 1 g of PQ is dissolved in 50 g of solvent 'A', $Δ T_{b}$ was 1.176 K while when 1 g of $PQ_{2}$ is dissolved in 50 g of solvent 'A', …
JEE Main 2026View solution →
Consider a solution of $CO_{2} (g)$ dissolved in water in a closed container.

Which one of the following plots correctly represents variation of log (partial pressure of CO2 in vapour phase above water) [y-axis] with log (mole fraction of $CO_{2}$ …
JEE Main 2026View solution →
Given below are two statements:

Statement I: The Henry's law constant $K_{H}$ is constant with respect to variations in solution's concentration over the range for which the solutions is ideally dilute.
Statement II : $K_{H}$ does not diff …
JEE Main 2026View solution →
The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is $____$ $g L^{- 1}$ . (Nearest integer)

Given: …
JEE Main 2026View solution →
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass $= 300 g mol^{- 1}$ ) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____$ $\times 1 0^{- 2}$ . (Nearest integer)
[Giv …
JEE Main 2026View solution →
Which one of the following graphs accurately represents the plot of partial pressure of $CS_{2}$ vs its mole fraction in a mixture of acetone and $CS_{2}$ at constant temperature ?
JEE Main 2026View solution →